University of Twente Student Theses


Modelling and analysis of reliability and long run availability of a fleet of rolling stock

Teshome, M.M. (2012) Modelling and analysis of reliability and long run availability of a fleet of rolling stock.

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Abstract:Availability of the fleet of a rolling stock company is an important and noticeable aspect for customers of these companies, which makes this availability a key aspect for the success. For the Netherland Railways (NS) that run multiple train units in rail network, predicting and keeping a required level of fleet availability is a challenging task. The stochastic nature of train breakdowns and the corrective maintenance to fix them are problems to keep track of availability of the fleet. If more trains are withdrawn from a fleet due to failure, the fleet operator, NS cannot provide the required transportation capacity to cover the scheduled services. To enhance the availability of the fleet, NS keeps a large fleet of trains. Each day NS keeps 200 operational and 3 cold standby trains in one of their service region. Standby trains are spare trains available in case of one of the operational trains fail. However keeping a high number of spare trains each costing about 2 million Euros is not economical. The different challenges at NS lead to the following problem statement: Given a repairable fleet of trains with cold standbys how do we model mathematically the long run fleet availability. To solve this problem a mathematical model has been created. The model was created using a method where a Markovian analysis is applicable to present the operation of the fleet system. It was designed to establish relationships between system availability, number of cold standby trains, failure rate and repair throughput time of the repair facility. The created model plans to evaluate the key performance indicators of the fleet system. The key performance indicators of the fleet that are included are:  Steady state fleet availability (SSA),  The mean time to failure (MTTF) and  The mean time to recover (MTTR). The steady state availability indicates the long run probability of the fleet working in a non-short mode state. In the non-short mode state, there are enough trains to satisfy the required transportation capacity. In other words, when a train fails there is a standby train ready to use. The mean time to failure indicates the average length of time that the fleet stays in the full operational state before going to the short mode state. On the other hand, the mean time to recover (MTTR) indicates the average length of time that the fleet stays in the failed states before going to the non-short mode state. In fact, emphasises was also given for evaluating the impact of spare trains on the average fleet availability. The created model is translated in to an algorithm. Our algorithm is encoded in the matlab software package. The model needs multiple parameters for which some of the values are estimations. The consequence for the results is that they might not match reality exactly. However, although the results might differ from reality, the effects of different types of decisions can still be derived from the results. The developed program accepts the fleet size ( ), the number of spare trains ( ), the failure rate ( ), the repair rate ( ), and the number of repair facilities ( as an input and produces all the values of the key performance indicators as an output. The size of the input values can be of any arbitrary number. Regardless of the size of the input, our program can perform well with a reasonable time. The model is computationally efficient. The program generates graphs of the steady state availability as a function of number of failed trains and Fleet availability as a function of number of standby trains. To obtain more managerial insights different scenario analyses have been done. For any given failure rate of a fleet the impact of varying the repair parameter was examined in relation to the associated numbers of spare trains. The model illustrates that the relationships between the failure rate, the number of spare trains, the repair throughput time and the corresponding relative utilization of the repair facilities, provide useful criteria for evaluating the availability of the fleet system. For one of the scenario, even with high number of spares the rate of output of the repair facilities being less than the average rate of failures doesn’t improve the fleet availability. In addition, the system is likely to prove uneconomic. For the other scenario where the rate of output of the repair facility being greater than the failure rate, by increasing the number of cold standby trains significant improvement in fleet availability can be obtained. The values of the parameters concerning the fleet availability at NS were inserted and a result using the Matlab algorithm was generated. The result demonstrated that for a fleet size of 200 trains and with 2 repair facilities keeping more than 2 standby trains is an over estimation. The evaluations show that with 2 cold standby trains the average fleet availability almost reaches 100%. This has an improvement potential of one train per the given region (33 %), which is about 2 million Euros. Our model can be also used to compute the fleet availability of the remaining service regions of the NS. Taken all the above into account, this research leaves further research directions as follows. In the future, considering multiple failure modes per corrective maintenance, analysing the impact of availability and limitation of spare parts at the maintenance depots, logistical and administrative delays at the repair facility would be interesting to research. A cost model subject to the highest attainable level of fleet availability and an in-depth study on the different types of maintenance activities at the repair shop would also be the right research direction.
Item Type:Essay (Master)
Faculty:BMS: Behavioural, Management and Social Sciences
Subject:52 mechanical engineering
Programme:Industrial Engineering and Management MSc (60029)
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